how to calculate d (distance of a code) for a code?

how to calculate d (distance of a code) for a code?

abdulmajeed (guest) 26 Jan 2013 10:08

is the distance of a code the same as the repetition of the parities in the code?
for example : (x,y) —-> (x,y,z,x,y,z,x,y,z) z is parity = (9,2,1) or (9,2,3)?

Guest (guest) 26 Jan 2013 10:57

With a data made of only two bits, you can easily find the distance by simply writing all four words and checking manually:

000000000
011011011
101101101
110110110

And since its a linear code, you can simply check the distance of all the other words from 0, as you can see it isn't 1 nor 3.

random.randstudent() (guest) 29 Jan 2013 17:56

You could also just check what happens if you flip x or flip y from 0 to 1.
If you flip x for example, all reptitions of x must change and also the parity (z) must change aswell.
The number of changes is 6 so d=6.